波动率衍生品是管理市场波动风险的主要产品之一，其中波动率指数(Volatility Index,VIX)产品和Switch Corridor产品作为两个典型的衍生品备受关注，但是现有的数值方法存在计算工作量大，数值稳定性差，收敛速度较慢等不足。本项目以这两个产品作为主要研究对象，基于柳树法的现有理论和方法，结合Monte Carlo精确模拟抽样理论和加速技术，通过矩匹配和降维等方法，提高现有柳树法处理高维问题的能力，计算速度和计算精度，并分析其在处理高维问题时的误差、稳定性和收敛性，并结合自动微分技术设计有效的风险管理算法。从而提出一套多资产路径相关的波动率衍生品定价和风险管理的理论方法和算法，为我国未来发展以波动率为标的的衍生品的定价和风险管理提供重要的技术储备。

Volatility derivatives are one of the main products to manage the risk of market volatility. Volatility Index (VIX) products and Switch Corridor products have attracted much attention as two typical volatility derivatives. However, the existing numerical methods have large calculation amount, poor numerical stability and slow convergence. This project will focus on the pricing and risk management of these two products. Based on the existing theories of the willow tree method, we will greatly improve the ability of the willow method to handle the high-dimensional problems, by combining Monte Carlo exact simulation theory with acceleration technology, and using the methods of moment matching and dimension reduction. We also analyze the error, stability and convergence of the algorithm when dealing with high-dimensional problems, and improve the calculation speed and accuracy. In addition, we design an effective risk management algorithm combined with automatic differentiation technology. Therefore, we propose a set of theoretical methods and algorithms for pricing and risk management of volatility derivatives which are multi-asset and path-related. This research will provide an important technical reference for the future development of pricing and risk management of Chinese derivatives based on volatility.